What is the vertices x^2-y^2-4x+8y-21=0 ?

The vertices x^2-y^2-4x+8y-21=0 is (5,4),(-1,4)

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vertices x^2-y^2-4x+8y-21=0

vertices

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

(5, 4), (- 1, 4)

Solution steps

(h + a, k), (h - a, k)

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x + 8 y - 21 = 0 :

Right-left Hyperbola with

(h, k) = (2, 4), a = 3, b = 3

(2 + 3, 4), (2 - 3, 4)

Refine

(5, 4), (- 1, 4)

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

10 x^{2} - 25 y^{2} = 100

\frac{y ^{2}}{64} - \frac{x ^{2}}{36} = 1

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

\frac{y ^{2}}{1} - \frac{x ^{2}}{15} = 1

What is the vertices x^2-y^2-4x+8y-21=0 ?
The vertices x^2-y^2-4x+8y-21=0 is (5,4),(-1,4)